Solve x-2/5+3x-1/4=2x+1/2

$$\frac{ x-2 }{ 5 } + \frac{ 3x-1 }{ 4 } = \frac{ 2x+1 }{ 2 }$$

Solve for x

$$x=-23$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 5,4,2.

$$4\left(x-2\right)+5\left(3x-1\right)=10\left(2x+1\right)$$

Use the distributive property to multiply 4 by x-2.

$$4x-8+5\left(3x-1\right)=10\left(2x+1\right)$$

Use the distributive property to multiply 5 by 3x-1.

$$4x-8+15x-5=10\left(2x+1\right)$$

Combine 4x and 15x to get 19x.

$$19x-8-5=10\left(2x+1\right)$$

Subtract 5 from -8 to get -13.

$$19x-13=10\left(2x+1\right)$$

Use the distributive property to multiply 10 by 2x+1.

$$19x-13=20x+10$$

Subtract 20x from both sides.

$$19x-13-20x=10$$

Combine 19x and -20x to get -x.

$$-x-13=10$$

Add 13 to both sides.

$$-x=10+13$$

Add 10 and 13 to get 23.

$$-x=23$$

Multiply both sides by -1.

$$x=-23$$